Solution
= Solution
\b[True.] The negative-level <hitting times> from the preceding calculation are almost surely finite for every negative integer, and occur at unbounded times. Therefore
$$
\boxed{\mathbb P\bigl(B_t\text{ does not converge to }+\infty\bigr)=1.}
$$
This is the almost-sure negation in the original PDF, not another assertion of convergence. The stronger oscillation statement $\liminf B_t=-\infty$ and $\limsup B_t=+\infty$ rules out that convergence path by path.